From time to time, offshore structures in the form of large offshore platforms are erected on the ocean floor for drilling wells in the development of oil and gas formations. The majority of offshore platforms that have been built and are in use today have been fabricated as single-piece units. One-piece platforms have been constructed for use in waters up to 1353 feet. However, it is necessary to build a special barge on which the platform rests when it is towed to its location offshore to move a platform structure of this length. Because of the weight and size of these large one-piece structures, it has been found desirable to design lighter structures having a central tower and having a plurality of supporting struts which extend from the central platform or working deck of the structure down to the ocean floor. Such structures are well known to the art and have been disclosed in U.S. Pat. Nos. 3,852,969 to Gibson et al; 2,597,110 to Lacy; 3,178,892 to Stimson; 4,557,629 to Meek et al; and 4,553,878 to Willemse et al. In many of these structures, the legs or struts supporting the platform above the surface of the water extend upwardly through the water surface and are hinged or otherwise connected to the platform. This brings the upper ends of all of the legs or struts into the wave action at the surface, thereby increasing the stress and corrosion problems on the platform. Other known structures that connect the central column to downwardly supporting struts have a base member or mat on the ocean floor that rigidly connects the lower ends of all the struts together and to the central column passing down through the struts.